Abstract: Let P be a finite poset. Consider two probability distributions on P: the uniform distribution; and the distribution where each element occurs with probability proportional to the number of maximal chains passing through it. Reiner, Tenner, and Yong observed that for many posets P of interest to algebraic combinatorialists, the expected Hasse diagram down-degree is the same for both these distributions. They called this the "coincidental down-degree expectations" (CDE) property for posets. I will review the history of the study of CDE posets: its origins in the algebraic geometry of curves, its connections to the tableaux/symmetric function/Schubert calculus world, etc. I will also present the "toggle perspective," which has been useful in establishing that various distributive lattices are CDE. Time permitting I will explain a forthcoming proof of a conjecture of Reiner-Tenner-Yong which says that certain weak order intervals corresponding to vexillary permutations are CDE. The proof involves expanding the "toggle perspective" to the setting of semidistributive lattices (following Barnard and Thomas-Williams).